Saiprasad Ravishankar

MR Image Reconstruction From Highly Undersampled k-Space Data by Dictionary Learning

Compressed sensing (CS) utilizes the sparsity of magnetic resonance (MR) images to enable accurate reconstruction from undersampled k-space data. Recent CS methods have employed analytical sparsifying transforms such as wavelets, curvelets, and finite differences. In this paper, we propose a novel framework for adaptively learning the sparsifying transform (dictionary), and reconstructing the image simultaneously from highly undersampled k-space data. The sparsity in this framework is enforced on overlapping image patches emphasizing local structure. Moreover, the dictionary is adapted to the particular image instance thereby favoring better sparsities and consequently much higher undersampling rates. The proposed alternating reconstruction algorithm learns the sparsifying dictionary, and uses it to remove aliasing and noise in one step, and subsequently restores and fills-in the k-space data in the other step. Numerical experiments are conducted on MR images and on real MR data of several anatomies with a variety of sampling schemes. The results demonstrate dramatic improvements on the order of 4-18 dB in reconstruction error and doubling of the acceptable undersampling factor using the proposed adaptive dictionary as compared to previous CS methods. These improvements persist over a wide range of practical data signal-to-noise ratios, without any parameter tuning.

Automated feature extraction for early detection of diabetic retinopathy in fundus images

Automated detection of lesions in retinal images can assist in early diagnosis and screening of a common disease: Diabetic Retinopathy. A robust and computationally efficient approach for the localization of the different features and lesions in a fundus retinal image is presented in this paper. Since many features have common intensity properties, geometric features and correlations are used to distinguish between them. We propose a new constraint for optic disk detection where we first detect the major blood vessels and use the intersection of these to find the approximate location of the optic disk. This is further localized using color properties. We also show that many of the features such as the blood vessels, exudates and microaneurysms and hemorrhages can be detected quite accurately using different morphological operations applied appropriately. Extensive evaluation of the algorithm on a database of 516 images with varied contrast, illumination and disease stages yields 97.1% success rate for optic disk localization, a sensitivity and specificity of 95.7%and 94.2%respectively for exudate detection and 95.1% and 90.5% for microaneurysm/hemorrhage detection. These compare very favorably with existing systems and promise real deployment of these systems.

Learning Sparsifying Transforms

The sparsity of signals and images in a certain transform domain or dictionary has been exploited in many applications in signal and image processing. Analytical sparsifying transforms such as Wavelets and DCT have been widely used in compression standards. Recently, synthesis sparsifying dictionaries that are directly adapted to the data have become popular especially in applications such as image denoising, inpainting, and medical image reconstruction. While there has been extensive research on learning synthesis dictionaries and some recent work on learning analysis dictionaries, the idea of learning sparsifying transforms has received no attention. In this work, we propose novel problem formulations for learning sparsifying transforms from data. The proposed alternating minimization algorithms give rise to well-conditioned square transforms. We show the superiority of our approach over analytical sparsifying transforms such as the DCT for signal and image representation. We also show promising performance in signal denoising using the learnt sparsifying transforms. The proposed approach is much faster than previous approaches involving learnt synthesis, or analysis dictionaries.

Structured Overcomplete Sparsifying Transform Learning with Convergence Guarantees and Applications

In recent years, sparse signal modeling, especially using the synthesis model has been popular. Sparse coding in the synthesis model is however, NP-hard. Recently, interest has turned to the sparsifying transform model, for which sparse coding is cheap. However, natural images typically contain diverse textures that cannot be sparsified well by a single transform. Hence, in this work, we propose a union of sparsifying transforms model. Sparse coding in this model reduces to a form of clustering. The proposed model is also equivalent to a structured overcomplete sparsifying transform model with block cosparsity, dubbed OCTOBOS. The alternating algorithm introduced for learning such transforms involves simple closed-form solutions. A theoretical analysis provides a convergence guarantee for this algorithm. It is shown to be globally convergent to the set of partial minimizers of the non-convex learning problem. We also show that under certain conditions, the algorithm converges to the set of stationary points of the overall objective. When applied to images, the algorithm learns a collection of well-conditioned square transforms, and a good clustering of patches or textures. The resulting sparse representations for the images are much better than those obtained with a single learned transform, or with analytical transforms. We show the promising performance of the proposed approach in image denoising, which compares quite favorably with approaches involving a single learned square transform or an overcomplete synthesis dictionary, or gaussian mixture models. The proposed denoising method is also faster than the synthesis dictionary based approach.

Learning Doubly Sparse Transforms for Images

The sparsity of images in a transform domain or dictionary has been exploited in many applications in image processing. For example, analytical sparsifying transforms, such as wavelets and discrete cosine transform (DCT), have been extensively used in compression standards. Recently, synthesis sparsifying dictionaries that are directly adapted to the data have become popular especially in applications such as image denoising. Following up on our recent research, where we introduced the idea of learning square sparsifying transforms, we propose here novel problem formulations for learning doubly sparse transforms for signals or image patches. These transforms are a product of a fixed, fast analytic transform such as the DCT, and an adaptive matrix constrained to be sparse. Such transforms can be learnt, stored, and implemented efficiently. We show the superior promise of our learnt transforms as compared with analytical sparsifying transforms such as the DCT for image representation. We also show promising performance in image denoising that compares favorably with approaches involving learnt synthesis dictionaries such as the K-SVD algorithm. The proposed approach is also much faster than K-SVD denoising.

Efficient Blind Compressed Sensing Using Sparsifying Transforms with Convergence Guarantees and Application to Magnetic Resonance Imaging

Natural signals and images are well known to be approximately sparse in transform domains such as wavelets and discrete cosine transform. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undersampled measurements. In this work, we focus on blind compressed sensing, where the underlying sparsifying transform is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the sparsifying transform from highly undersampled measurements. The proposed block coordinate descent-type algorithms involve highly efficient optimal updates. Importantly, we prove that although the proposed blind compressed sensing formulations are highly nonconvex, our algorithms are globally convergent (i.e., they converge from any initialization) to the set of critical points of the objectives def...

Sparsifying transform learning for Compressed Sensing MRI

Compressed Sensing (CS) enables magnetic resonance imaging (MRI) at high undersampling by exploiting the sparsity of MR images in a certain transform domain or dictionary. Recent approaches adapt such dictionaries to data. While adaptive synthesis dictionaries have shown promise in CS based MRI, the idea of learning sparsifying transforms has not received much attention. In this paper, we propose a novel framework for MR image reconstruction that simultaneously adapts the transform and reconstructs the image from highly undersampled k-space measurements. The proposed approach is significantly faster (>10x) than previous approaches involving synthesis dictionaries, while also providing comparable or better reconstruction quality. This makes it more amenable for adoption for clinical use.

Learning overcomplete sparsifying transforms for signal processing

Adaptive sparse representations have been very popular in numerous applications in recent years. The learning of synthesis sparsifying dictionaries has particularly received much attention, and such adaptive dictionaries have been shown to be useful in applications such as image denoising, and magnetic resonance image reconstruction. In this work, we focus on the alternative sparsifying transform model, for which sparse coding is cheap and exact, and study the learning of tall or overcomplete sparsifying transforms from data. We propose various penalties that control the sparsifying ability, condition number, and incoherence of the learnt transforms. Our alternating algorithm for transform learning converges empirically, and significantly improves the quality of the learnt transform over the iterations. We present examples demonstrating the promising performance of adaptive overcomplete transforms over adaptive overcomplete synthesis dictionaries learnt using K-SVD, in the application of image denoising.

Online Sparsifying Transform Learning— Part I: Algorithms

Techniques exploiting the sparsity of signals in a transform domain or dictionary have been popular in signal processing. Adaptive synthesis dictionaries have been shown to be useful in applications such as signal denoising, and medical image reconstruction. More recently, the learning of sparsifying transforms for data has received interest. The sparsifying transform model allows for cheap and exact computations. In this paper, we develop a methodology for online learning of square sparsifying transforms. Such online learning can be particularly useful when dealing with big data, and for signal processing applications such as real-time sparse representation and denoising. The proposed transform learning algorithms are shown to have a much lower computational cost than online synthesis dictionary learning. In practice, the sequential learning of a sparsifying transform typically converges faster than batch mode transform learning. Preliminary experiments show the usefulness of the proposed schemes for sparse representation, and denoising.

Closed-form solutions within sparsifying transform learning

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image denoising, and medical image reconstruction. In this work, we focus specifically on the learning of orthonormal as well as well-conditioned square sparsifying transforms. The proposed algorithms alternate between a sparse coding step, and a transform update step. We derive the exact analytical solution for each of these steps. Adaptive well-conditioned transforms are shown to perform better in applications compared to adapted orthonormal ones. Moreover, the closed form solution for the transform update step achieves the global minimum in that step, and also provides speedups over iterative solutions involving conjugate gradients. We also present examples illustrating the promising performance and significant speed-ups of transform learning over synthesis K-SVD in image denoising.